|
Abstract
|
In this paper, we study the nonlinear sin4(?) system in 1 1 dimensions which exhibits interesting nonlinear properties. We have categorized the system as radiative, since the collision of a kink and an antikink with velocities less than a threshold velocity leads to the complete annihilation of the pair and production of two high-amplitude wave packets with zero topological charges. Our results show that the individual kinks and antikinks are stable even against strong (nonlinear) perturbations. Other radiative systems similar to the sin4(?) system are also studied. Finally, linear perturbations about the kink solution are examined in relation to the relaxation problem, by looking for the bound states of the resulting Schr¨odinger-like equation. Interestingly enough, the sin4(?) system has only one trivial bound state with the ?^2 eigenvalue residing exactly at the top of the potential well. The significance of this property on the relaxation of the kink in this system is examined and compared to other nonlinear systems.
|